This paper deals with fractional-order controllers. We outline mathematical description of fractional controllers and methods of their synthesis and application. Synthesis method is a modified root locus method for fractional-order systems and fractionalorder controllers. In the next section we describe how to apply the fractional controller on control systems.

Fractional order dynamic model could model various real materials more adequately than integer order ones and provide a more adequate description of many actual dynamical processes. Fractional order controller is naturally suitable for these fractional order models. In this paper, a fractional order PID controller design method is proposed for a class of fractional order system models. Better p...

Although some numerical methods of the fractional-order chaotic systems have been announced, high-precision always direction that researchers strive to pursue. Based on this problem, paper introduces a approach. Some complex dynamic behavior Lorenz are shown by using present method. We observe novel in experiments which unlike any previously discovered or theoretical studies. investigate influe...

Synchronization of coupled nonidentical fractional-order hyperchaotic systems is addressed by the active sliding mode method. By designing an active sliding mode controller and choosing proper control parameters, the master and slave systems are synchronized. Furthermore, synchronizing fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system is performed to show...

The theory of derivative of noninteger order goes back to Leibniz, Liouville, Riemann, Grunwald and Letnikov. Derivatives of fractional order have found many applications in recent studies in mechanics, physics, economics, medicine.Classes of fractional differentiable systems have studied in [10], [4]. In the first section the fractional tangent bundle to a differentiable manifold is defined, u...

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we...

There is an increasing interest in dynamic systems and controls of noninteger orders or fractional orders. Clearly, for closed-loop control systems, there are four situations. They are 1) IO (integer order) plant with IO controller; 2) IO plant with FO (fractional order) controller; 3) FO plant with IO controller and 4) FO plant with FO controller. However, from engineering point of view, doing...